geno3141

If you had 20 dogs and you lost 11 of these dogs, you would still have  20 - 11  =  9 dogs.

Instead of dogs, you have sqrt(3)s   --->   20 sqrt(3)  -  11 sqrt(3)  =  (20 - 11) sqrt(3)  =  9 sqrt(3).

To find the percent of error:

1)  find the difference of the real value from the expected value:  75 - 50  =  25

2)  divide that answer by the expected value:  25 / 50  =  0.50

3)  change this number into a percentage:  0.50   --->   50%

Find the inverse of both sides:  h^-1( h( x⁴ + 1 ) )  =  h^-1( h( x² + 3 ) )

--->   x⁴ + 1  =  x² + 3

--->   x⁴ - x² - 2 =  0

--->   (x² - 2)(x² + 1)  =  0

--->   x² - 2  =  0     or     x² + 1  =  0

--->   x  =  + sqrt(2),  -sqrt(2),  +sqrt(-1),  -sqrt(-1)

With an equation that looks like this:  -4(x + 8)  =  16

If you distribute the -4 on the left side, you get this:  -4x - 32  =  16.

You distribute the -4 on the left side, but, at this time, YOU DO NOTHING TO THE RIGHT SIDE.

I would choose 'D'.

The mode is the number used the most often; for this set of data, the mode is 83.8 (which is used 6 times).

Adding 84.3 does not change the mode, it will still be 83.8.

For a thorough answer see pages 6 - 16 of:  

https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap-calculus-course-description.pdf

For a quick overview:  limits, integration (finding the area under a graphed curve in two dimensitons and the volume under a graphed curve in three dimensions, with applications), differentiation (finding the slope of a tangent line of a graphed curve, with applications), and infinite series (with applications).

Since the probability for each one is defective is 0.05,

the probability for all three to be defective:  0.05 x 0.05 x 0.05  =  0.000 125

Since the probability that each one is not defective is 0.95, 

the probability for all three to not be defective:  0.95 x 0.95 x 0.95 = 0.857 375

A prime number is a whole number (counting number, natural number) that is larger than 1 but only divisible by itself and 1.

Some prime numbers are 2, 3, 5, 7, 11, ..

4 is not a prime number because it is the product of 2 x 2 as well as 1 x 4.

6 is not a prime number because it is the produt of 2 x 3 as well as 1 x 6.

2 is a prime number because the only product is 1 x 2.

3 is a prime number because the only product is 1 x 3.

If the number is a prime number it can only be factored into 1 and itself.

A number is not a prime number if it can also be factored in a different way besides 1 and itself.

Since  f(x) = ax/(2x+3),  to find  f( f(x) ), replace the x=term in  ax/(2x+3)  wwith  ax/2x+3):

f( f(x) )  =  f( ax/(2x+3) )  =  [ a( ax/(2x+3) ) ] / [ 2( ax/(2x+3) ) + 3 ]

    =   [ a²x / (2x+3) ] / [ 2ax / (2x+3) + 3]

Assume that  x  isn't  -3/2:  multiply both the numerator and denominator by  2x + 3 and simplify:

    =  a²x / ( 2ax + 3(2x+3) ]

    =  a²x / ( 2ax + 6x + 9 ]

Since f( f(x) ) = x:     a²x / ( 2ax + 6x + 9 ]  =  x

Multiply both sides by  2ax + 6x + 9:     a²x  =  x(2ax + 6x + 9)

Assuming that x isn't 0, divide both sides by x:     a²  =  2ax + 6x + 9

--->     2ax + 6x  =  a² - 9

--->    2x(a + 3)  =  (a + 3)(a - 3)

If a is not equal to -3, divide both sides by  a + 3:

--->   2x  =  a - 3

and    x  =  (a - 3) / 2                        

But, x could be zero (it checks in the original expression).

Also checking  -3/2  and  -3 -- they don't check.

So, the answer:  either  0  or  (a - 3)/2.

How many groups of 9 students are there in a school of 1080 students?

1080 divided by 9 gives an answer of 120.

On average, in each of these 120 groups 5 voted for the same person:  120 x 5  = 600.

So, 600 voted for the winning candidate.

Checking:  600 / 1080  =  5/9.